A method of this type is known for example from DE 100 19 277 A1. In this method a radio link is established for transmitting data between an electronic key module to be carried by and on the user and an evaluation unit provided in a motor vehicle, in order to identify the key module based on an identification number stored in the key module, and to release, if necessary, the motor vehicle for use. The radio link is established here via a transmitting and receiving station provided in the key module and in the evaluation unit. To prevent the radio link from being extended via relay stations and to release the motor vehicle in this way without being noticed by the authorized user, the distance between the key module and the evaluation unit is determined and the release of the motor vehicle is prevented, if the key module is not within the immediate vicinity of the evaluation unit. In this case, determination of the distance is based on an evaluation of the signal running time of the signals transmitted via the radio link.